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- W2034264869 abstract "In this paper we establish a multiplicity result concerning the existence of doubly periodic solutions in a $$2times 2$$ nonlinear elliptic system arising in the study of self-dual non-Abelian Chern–Simons vortices. We show that the system admits at least two solutions when the Chern–Simons coupling parameter $$kappa >0$$ is sufficiently small; while no solution exists for $$kappa >0$$ sufficiently large. As in Nolasco and Tarantello (Commun Math Phys 213:599–639, 2000), we use a variational formulation of the problem. Thus, we obtain a first solution via a constrained minimization method and show that it is asymptotically gauge-equivalent to the (broken) principal embedding vacuum of the system, as $$kappa rightarrow 0$$ . Then we obtain a second solution by a min-max procedure of “mountain pass” type." @default.
- W2034264869 created "2016-06-24" @default.
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- W2034264869 date "2013-03-31" @default.
- W2034264869 modified "2023-10-14" @default.
- W2034264869 title "Doubly periodic self-dual vortices in a relativistic non-Abelian Chern–Simons model" @default.
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- W2034264869 doi "https://doi.org/10.1007/s00526-013-0615-7" @default.
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